Mean, median, mode – what is average?

The three months or so before the November 2007 elections, I came home every day to find more new political postcards waiting for me in my mail box — usually 3 or 4 per day.  It just happens that I live in a state senate district that is very much divided.  The liberals put forth the most liberal candidate they could find, the conservatives did much the opposite.  And just about every group possible wanted their opinion heard.  Most did so in an honest, effective way, but a few were downright dishonest liars.

I count among the liars the state branch of the National Educators Association (NEA).  You see, they were advocating for the liberal candidate for fear that a conservative candidate would be less favorable toward their perspective when it came to the state budget.

Mean is adding all the numbers and dividing by the number of sets you just added. This is what most people think of when they hear average.

Median is lining up all the number sets and picking the one in the middle.

Mode is the most common number in a set. In most professions, there are going to be more 1st year workers than any other year.

I wish I had kept a copy of their postcard, but it said something akin to “Candidate XYZ wants to destroy education in our state.  The average teacher makes $26,000 per year.  Blah, blah, blah.”  The key part is what they said that the average teacher makes.  I’ll admit, $26,000 isn’t much and it would be difficult to raise a family on that.  Why would anyone choose to be a teacher with that type of income?  I didn’t think we’d have nearly enough to staff our schools based on those numbers, so I did a little research.

The number that the teacher’s union put forth was exactly the base 1st year starting salary for teachers.  I was taken back by that — how could this be average?  Surely teachers get raises based on years experience, furthering their education, and merit base pay, right?

It didn’t take me long to figure out that what they meant by average was not the same as what anyone else would mean by average.

Mean, median, mode — what is average?  Most people are familiar with mean:  Add up the numbers, then divide by how many sets of numbers you added.  Median is simply lining up all the numbers and picking the one in the middle.  Mode is the most common number in a number set.  The teacher’s union used mode.

In the teaching profession, as in just about any other profession, you are going to have more first year teachers than you are teachers in exactly their 7th year or teachers in exactly their 25th year.  If the teacher population is stable, the number of first year teachers must equal the sum of all the teachers who left from the previous year.

When the teacher’s union lined up all the salaries of all the teachers in the state, they said average but used mode.  True?  Perhaps.  Dishonest?  Absolutely!  But hey, they had to lie to get their candidate elected.

I suspect that if they used mean or median (more honest measures of average in this example), their postcard would have backfired — teachers in my district make much more money than the average worker.  It would be rubbing it in, “We have an employer with a virtually endless supply of money and we can extract as much as we want from them.”  Outside of government employees, not even other unions have this “benefit”.

The thing is, if the members of this teacher union are suppose to be educating my children, it is a little upsetting that they would be so dishonest.  Is it too much a burden to expect our teachers to at least tell the truth without distortions?

It is truly deplorable that teachers rely on a failed education system that cannot even teach mean, median, and mode to distort the truth to get what they want.

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2 Comments

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2 responses to “Mean, median, mode – what is average?

  1. kourtnie

    I am a teacher and I just learned what these kinds of averages are. I don’t agree with you on everything, but I can see where we (as teachers) need to approve.

  2. Katie

    I learned more about math reading your article than I have in 16 years of public education (including college). Thanks!